Computing Multifractal Spectrum of Images

Computing the multifractal spectrum of images. It represents fractal parameters for multiscale measurement of fractal characteristics. The multifractal spectrum provides insights into the fractal properties of images at different scales, revealing how local scaling behaviors vary across the image domain. Through multifractal spectrum computation, we obtain detailed fractal information that enhances our understanding of image structure and complexity. The calculation process typically involves partitioning the image into boxes of varying sizes, computing measure densities, and analyzing the singularity spectrum using Legendre transformation. This technique finds applications in image processing, pattern recognition, and image analysis, where it helps improve image understanding and analytical capabilities by characterizing texture complexity, detecting anomalies, and quantifying structural heterogeneity. Common implementation approaches include using box-counting algorithms with different moment orders (q-values) to compute the generalized dimension spectrum.